Return to Main
Page
JOINT
CSHRP/NEW BRUNSWICK BAYESIAN APPLICATION 1.0 INTRODUCTION New Brunswick Department of
Transportation (NBDOT) annually collects rut data on the
provincial arterial highway system, providing a large
database that has received limited use. It was proposed
to use this large database with Bayesian modeling, which
combines prior knowledge and experience with data, to
predict rutting of the three different asphalt concrete
overlay techniques (thin overlay, thick overlay with
padding, and thick overlay with milling) used for asphalt
concrete pavement rehabilitation throughout the province.
The objective of this project was to demonstrate to the
NBDOT an application for Bayesian Modeling and not to
specifically present predictive models ready for design
application. A real inhouse problem was addressed to
optimize rehabilitation design of overlays with respect
to rutting. Development of the Bayesian rutting
models combined expert judgement with actual data. Expert
Judgement was solicited from paving experts to provide an
initial database which was analyzed using a classical
regression approach to produce a predictive model called
a "prior". The actual data base, referred to as
"data", was developed from information gathered
from various branches throughout the Department on the
selected variables. These two sources of information, the
"prior" and the "data", were then
combined through the Bayesian software to come up with a
model that was a combination of expert judgement and data
called the "posterior". The results of the first generation
models from this exercise were discussed with the
consultants to this project, Vemax Management Inc., at
the CanadianStrategic Highway Research Program
(CSHRP) Workshop in Ottawa in May 1995. Recommendations
were made on performing further iterations. As a result
of these recommendations the data bases for the thick
overlay rehabilitation were combined and were treated as
one method of rehabilitation. The second iteration
Therefore, addressed the models for only two overlay
rehabilitation strategies: thick and thin. 2.0 TEAM MEMBERS The NBDOT staff involved in the
Bayesian modeling application were lead analyst Michael
Jackart, and project team members Pam MacPhersonMunn
and Liane Callaghan. Nine experts were encoded from NBDOT
staff. Six experts were members of the NBDOT Pavement
Specification Rewrite Committee. The members of the
committee were from a broad range of backgrounds and
expertise each with 12 to 25 years of experience. The
members of the committee were: Paul Nicholson, Paving
Engineer; Terry Hughes, Assistant Paving Engineer; Andy
Legere, Laboratory Engineer; Drew Robertson, Resident
Engineer; Fred MacFarlane, Paving Technician; and Harold
Flemming, Regional Asphalt Technician. The three
remaining experts encoded were; Ray Leblanc Regional
Asphalt Technician; Ralph Doucet, Regional Asphalt
Technician and Rick Crandall, Senior Planning Technician.
Each expert was encoded for each of the three models. 3.0 METHODOLOGY The approach in the development of the
model was to prepare a specific model for each of the
three rehabilitation procedures. The methodology followed
for each model was the ten step template for building
Bayesian predictive models developed by CSHRP through
Decision Focus, Clayton Sparkes and Associates and Vemax
Management Inc. It was not the purpose of this project to
produce a definitive predictive rutting model; the
purpose was to evaluate Bayesian modeling as a viable
tool that could be used to predict performance in
general. The ten steps to the Bayesian Template are as follows:
3.1 Step 1 Decide What You Want
to Model The first step in the Bayesian modeling
development was to define exactly what was going to be
modeled. NBDOT annually collects rut data on the
provincial arterial highway system and has an extensive
database that has seen limited use in the past. It was
proposed to use this database to predict rutting on the
three different types of asphalt concrete rehabilitation
methods used throughout the province; thin overlay, thick
overlay with padding, thick overlay with milling. Rut
data collection will continue in the province on an
annual basis; therefore, it is possible to monitor the predictive
capabilities of the models annually as well as updating
the database and refining the models. 3.2 Step 2 Select Dependent Variable 3.3 Step 3 Select the Model Type Steps two and three were selection of
the dependent variable and selection of the model type
respectively. It was decided to follow the rut model
developed by the Canadian Long Term Pavement Performance
(CLTPP) project. The depth of rutting in millimeters
was selected as the dependent variable and the empirical
model type was used. 3.4 Step 4 Select Independent Variables Step four was selection of the
independent variables. A maximum of five to seven
independent variables are practical because as the number
of independent variables increases past this it is more
difficult to develop a prior. Another consideration to
selecting independent variables is choosing variables for
which there is data available. Therefore, considering the
purpose of this project and availability of data, it was
decided to use the same independent variables as the
CLTPP model . These included Age in years; Thickness
measured in millimeters; % Air Voids; % Retained on the
4.75mm sieve; % Crushed particles and Traffic measured in
KESAL/ year. 3.5 Step 5 Postulate Functional Form The next step was to postulate the
functional form. A simple linear form was chosen
initially but after running the data through the XLBayes
program (1) ( the XLBayes program is an addin module
for Microsoft EXCEL 5.0 that performs Bayesian regression
analysis, written by Mark Nickeson, Vemax Management
Inc.), it was found that a log transformation on the
traffic variable was required. Therefore the resultant
functional form was modified to curvilinear. The term
curvilinear is the term used by Vemax Management Inc
when referring to models that contain at least one
transform and result in the dependent variable (Y) not
being a straight line relation with every independent
variable (Xi's). This term was used to facilitate their
discussions and is not standard convention. 3.6 Step 6 Assemble Information The sixth step was to assemble the
information for both the sample database,
"data" and for the calculation of the
"prior". Collecting the actual sample database
was the most time consuming aspect of this project since
information was required from the Design, Construction,
Planning and Land Management and, Maintenance and Traffic
Branches. 3.6.1 Compiling Actual Sample Data
Base "Data" This database was compiled by obtaining
a list of paving contracts on arterial highways from the
Design Branch and sorting them into the type of
rehabilitation method used. Once a list of contracts was
compiled and sorted into the rehabilitation type,
information on the exact stationing of the contract, the
rate of asphalt application, the percent air voids in the
mix and the percent passing the 4.75mm sieve in the mix
were obtained for each contract from the Construction
Branch paving summaries. Rutting data was then gathered
from the Planning Branch and traffic data was collected
from the Maintenance and Traffic Branch. The traffic data
(counts and classifications) were obtained from
intersection traffic studies. These intersection counts
had to be entered into the NBDOT Equivalent Single Axle
Load (ESAL) Forecaster program 2 to obtain the ESAL
value. The ESAL value obtained from the ESAL Forecaster
program is based on the actual fleet distributions
obtained from the intersection counts and truck factors
that are area sensitive to four specific types of hauling
use the highway would receive. Once all the data was collected and
entered into a spreadsheet for each model, quality
control measures were applied to the data. Only those
contracts with complete sets of independent variables and
corresponding dependent variable observations were
included. Any outlying data was removed after evaluation. 3.6.2 Encoding Expert Judgement to
Calculate the "Prior" The development of the prior model
first involved encoding the expert judgement to obtain
the expert judgement database. Nine experts were encoded,
including six (6) from the NBDOT Pavement Specification
Rewrite Committee and three additional experts from
NBDOT. These experts were initially asked for their input
on appropriate limits for each independent variable.
After meeting with the experts, an encoding package
similar to the CLTPP encoding package was prepared for
each of the three different models (See Appendix A). Each
of the nine experts was encoded on a 48 cell full
orthogonal matrix specific for each type of
rehabilitation. Once the experts were encoded, there was
a group review of the results of the encoded information
to see if results actually reflected the experts
opinions. This meeting identified consensus and
differences in the expert judgement and was a crucial
step in building confidence in the priors. 3.7 Steps 7 10 Perform Bayes, Use
Models to Predict Performance, Evaluate Model and
Iterations Steps seven through ten were performing
the analysis and then evaluating and iterating the model.
These steps are explained in more detail in the following
sections which describe each iteration. |